We identify a class maximal dissipative solutions to models of compressible viscous fluids that maximize the energy dissipation rate. Then we show any solution approaches an equilibrium state for large times.

The controlled rotation of solid particles trapped in a liquid by an ultrasonic vortex beam is observed. Single polystyrene beads, or clusters, can be trapped against gravity while simultaneously rotated. The induced rotation of a single particle is compared to a torque balance model accounting for the acoustic response of the particle. The measured torque (∼ 10 pNm for a driving acoustic power...

A modification of the Roe scheme aimed at low Mach number flows is discussed. It improves the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is done by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scali...

A central question in the dynamics of vortex lines in superfluids is dissipation on approaching the zero temperature limit T→0. From both NMR measurements and vortex filament calculations, we find that vortex flow remains laminar up to large Reynolds numbers Re{α}∼10(3) in a cylinder filled with 3He-B. This is different from viscous fluids and superfluid 4He, where the corresponding responses a...

[1] In a series of numerical experiments, arrays of parallel-dipping normal faults formed only if the model contained a thin viscous layer sandwiched between the brittle, faulted layer on top and a lower boundary that resisted vertical displacement. With this particular vertical stratification, parallel-dipping faults developed even if the viscous layer had a shear-stress-free lower boundary co...

Capillary instability of a liquid cylinder immersed in another liquid is analyzed based on potential flow solutions. The growth rate of the instability is obtained by considering the normal stress balance at the interface. We derive a viscous correction of the irrotational pressure which presumably arises from a boundary layer needed to resolve the discontinuity of the tangential velocity and s...

The rate of viscous energy dissipation in a shear layer of incompressible Newtonian fluid with injection and suction is studied by means of exact solutions, nonlinear and linearized stability theory, and rigorous upper bounds. For large enough values of the injection angle a steady laminar flow is nonlinearly stable for all Reynolds numbers, while for small but nonzero angles the laminar flow i...

We study the time evolution of a sessile liquid droplet, which is initially put onto a solid surface in a nonequilibrium configuration and then evolves towards its equilibrium shape. We adapt here the standard approach to the dynamics of mechanical dissipative systems, in which the driving force, i.e., the gradient of the system’s Lagrangian function, is balanced against the rate of the dissipa...